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	<h1>Ordered categorical responses; The SOCATT data</h1>
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                     Code: <a href="socatt.tpl">socatt.tpl</a><br>
                     Data: 		<a href="socatt.dat">socatt.dat</a><br>
                     Initial values: <a href="socatt.pin">socatt.pin</a><br>
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                     All required files (DOS): <a href="socatt.zip">socatt.zip</a><br>
					 All required files (linux): <a href="socatt.tar.gz">socatt.tar.gz</a><br>					 
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                     Expected Results: <a href="socatt-expected-results.par">socatt.par</a><br>
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                     In a <a href="../admb_tutorial.html">DOS</a> window<br> 
					 Under <a href="../admb_tutorial.html">linux</a><br>			
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             <font face="Arial, Helvetica" color="White"><b>Results: Computation times</b></font>
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	<td>ADMB-RE</td>
	<td>30 seconds</td>
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	<td>aML</td>
	<td>10-15 seconds</td>
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	<td>SAS</td>
	<td>50-60seconds</td>
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	<td>MLwiN</td>
	<td>10-15 seconds</td>
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	<td>HLM 5</td>
	<td>50-60 seconds</td>
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	<td>MIXOR</td>
	<td>5-10 seconds</td>
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Computation times for other packages taken from <a HREF="http://multilevel.ioe.ac.uk/softrev/tables.html">here</a>.
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<h3><strong>Model description</strong></h3>
The SOCATT data set is used in the comparison of different software packages for multilevel modelling, conducted by 
the <a HREF="http://multilevel.ioe.ac.uk/softrev/index.html">Centre for Multilevel Modelling</a>.
The SOCATT data consist of the responses to a set of dichotomous items on a woman's right to have an abortion. 
The outcome variable (<em>y<sub>ij</sub></em>) is a score constructed from these items ranging from 1 to 7, with a higher score 
corresponding to stronger support for abortion. Each of 264 respondents was asked the same set of questions on four occasions, 
1983-1986, and <em>y<sub>ij</sub></em> denotes the response from individual <em>i</em> in year <em>j</em>. 
We consider one categorical covariate (religion) with 4 categories. A random intercept ordered logit model was fitted: 
<br><br>
<div align="center">logit[ P(<em>y<sub>ij</sub> < s</em>) ] = <em><FONT FACE="Symbol">k</FONT><sub>s</sub> + 
b<sub>1</sub>x<sub>i1</sub> + b<sub>2</sub>*x<sub>i2</sub> + b<sub>3</sub>*x<sub>i3</sub></em> + <em>u<sub>i</sub></em>, </div>
<div align="center"><em>u<sub>i</sub></em> ~ N(0,<em><FONT FACE="Symbol">s</FONT><sup>2</sup></em>)</div>
where <em>x<sub>1i</sub></em>, <em>x<sub>2i</sub></em> and <em>x<sub>3i</sub></em> are dummy variables coding for
the different levels of the categorical covariates, and <em><FONT FACE="Symbol">k</FONT><sub>s</sub></em> are threshold
parameters. A full description of the model can be found here: <a href="socatt.pdf">socatt.pdf</a><br><br><br>
 

<h3><strong>Results</strong></h3>
The following table shows the parameter estimates obtained with ADMB-RE.<br>
<br>

<div align="center"><table cellspacing="2" cellpadding="2" border="1" rules="cols">
<tr>
	<td><em><FONT FACE="Symbol">t</FONT><sub>1</sub></em></td>
	<td><em><FONT FACE="Symbol">t</FONT><sub>2</sub></em></td>
	<td><em><FONT FACE="Symbol">t</FONT><sub>3</sub></em></td>
	<td><em><FONT FACE="Symbol">t</FONT><sub>4</sub></em></td>
	<td><em><FONT FACE="Symbol">t</FONT><sub>5</sub></em></td>
	<td><em><FONT FACE="Symbol">t</FONT><sub>6</sub></em></td>
	<td><FONT FACE="Symbol">s</FONT></td>
	<td>b<sub>1</sub></td>
	<td>b<sub>2</sub></td>
	<td>b<sub>3</sub></td>
</tr>
<tr>
	<td>-4.13</td>
	<td>-2.39</td>
	<td>0.4</td>
	<td>1.34</td>
	<td>2.23</td>
	<td>3.27</td>
	<td>2.23</td>
	<td>1.95</td>
	<td>0.68</td>
	<td>2.78</td>
</tr>
</table>
</div><br>

Results for other software packages can be obtained
<a HREF="http://multilevel.ioe.ac.uk/softrev/tables.html">here</a>.
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